Theoretical Analysis of Electrostatic Effects on Ion Transport in Ultrathin Membranes

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Abstract
Ionic diffusion across surfactant bilayer membranes is strongly influenced by electrostatic image forces. An analysis that relates the potential energy barrier for ion transport and image effects is presented where the finite size of permeable ions is recognized, instead of assuming that ions are point charges. The analysis considers the bilayer membrane as a laminated dielectric sheet structure where the central hydrocarbon‐like core is interposed between two thinner layers that represent the polar head groups of the amphiphillic molecules that form the membrane. In the cases treated, the inner layer is approximately 30–70Å thick and has a dielectric constant of 2, while the polar layers are 5–10Å thick and have dielectric constants in the range 10–30. Permeable ions are represented as charged, perfectly conducting spheres whose diameter is determined by the polarizability of the associated ion species. The energy barrier due to image forces is computed by solving a set of Poisson's equations for the electrical potential within the sheet membrane and the surrounding aqueous electrolyte solution. The solution is obtained by using the method of images to determine infinite, but convergent, sets of image charges that arise from the polarizing effect of a permeable ion near the membrane‐solution interface. The results of a parametric study of this model show that the potential energy barrier is strongly dependent on the radius of the ion. The dielectric constant of the polar layer has a somewhat smaller effect within the range of values considered to be physically realistic for surfactant bilayer membranes.

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